Q 1: What is
the definition of the Ajnaby or Ajnabiyyah?
Is the uncle's son considered Ajnaby to his female cousin? Is it permissible for them to shake hands?
An Ajnaby man is a man who is not a Mahram (spouse or permanently unmarriageable relative) for a woman. The Mahrams are mentioned in the Ayah (Qur'anic Verse) which begins with:
And tell the believing women to lower their gaze (from looking at forbidden things)
This also applies to women. So, a male cousin is considered Ajnaby to a female cousin and it is unlawful for them to shake hands. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.